Warm-Up Math Social Studies P.E. Women Men 2 10

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Warm-Up Math Social Studies P.E. Women 16 6 8 Men 2 10 Math Social Studies P.E. Women 16 6 8 Men 2 10 What is the probability that a randomly selected person is a woman who likes P.E.? 2. Given that you select a man, what is the probability that he likes Social Studies? 3. What is the probability that you select a person who likes Math?

Quadratic Regression

Quadratic Model Is a quadratic function that represents a real data set. Models are useful for making estimates.

Quadratic Regression Last year, you used a calculator to perform linear regressions, exponential regressions, and made predictions using the models. You can apply a similar statistical method to make a quadratic model for a given data set using quadratic regression.

Coefficient of Determination R2 Shows how well a quadratic function model fits the data. The closer R2 is to 1, the better the fit. Example, in a model with R2  0.996 the quadratic model is a good fit.

The table shows the cost of circular plastic wading pools based on the pool’s diameter. Find a quadratic model for the cost of the pool, given its diameter. Use the model to estimate the cost of the pool with a diameter of 12 ft. Example 1: Diameter (ft) 4 5 6 7 Cost $19.95 $20.25 $25.00 $34.95

Example 1 Continued Step 1 Enter the data into two lists in the calculator. Step 2 Use the quadratic regression feature. 2nd Data, 5:

Example 1 Continued Use the model to estimate the cost of the pool with a diameter of 12 ft. Step 3 Table 1: f(12) enter ANSWER: For a diameter of 12 ft, the model estimates a cost of about $156.29.

Example 2 The tables shows approximate run times for 16 mm films, given the diameter of the film on the reel. Find a quadratic model for the reel length given the diameter of the film. Use the model to estimate the reel length for an 8-inch- diameter film. Film Run Times (16 mm) Diameter (in) Reel Length (ft) Run time (minutes) 5 200 5.55 7 400 11.12 9.25 600 16.67 10.5 800 22.22 12.25 1200 33.33 13.75 1600 45.25

Example 2 Continued Step 1 Enter the data into two lists in a calculator. Step 2 Use the quadratic regression feature.

Example 2 Continued Use the model to estimate the reel length for an 8-inch-diameter film. ANSWER: For a diameter of 8 in., the model estimates the reel length to be about 446 ft. Step 3 Table 1: f(8) enter

Write a quadratic function that fits the points (2, 0), (3, –2), and (5, –12). Example 3 f(x) = –x2 + 3x – 2

Practice Worksheets Quadratic regression